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33. Use properties 1–6 of logarithms to establish property 7: log 1/x = −log(x) for all x > 0.

User Soulsabr
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Answer:

The proprierties are explained in the step-by-step explanation.

Explanation:

We have the following logarithm proprierty:


\log{(a)/(b)} = \log{a} - \log{b}

And


\log{1} = 0

So, we apply these proprierties:


\log{(1)/(x)} = \log{1} - \log{x} = 0 - \log{x} = -\log{x}

Since the domain of
\log{x} is
x > 0, we have that


\log{(1)/(x)} = -\log{x}, x > 0

User Michael Baranov
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